The aim of this book is to study harmonic maps, minimal and
parallel mean curvature immersions in the presence of symmetry. In
several instances, the latter permits reduction of the original
elliptic variational problem to the qualitative study of certain
ordinary differential equations: the authors' primary objective is
to provide representative examples to illustrate these reduction
methods and their associated analysis with geometric and
The material covered by the book displays a solid interplay
involving geometry, analysis and topology: in particular, it
includes a basic presentation of 1-cohomogeneous equivariant
differential geometry and of the theory of harmonic maps between
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